Nonlinear optical properties of spatially distributed particle composites

Abstract

We examine the nonlinear dielectric response of small spherical grains ϵ m embedded in a linear dielectric ϵ d . The models for the spherical grains are a Kerr medium1,2 and a two-level system.3 The expression for the dielectric function ϵ m is dependent of the grain size; in addition it also depends on the local electric field E L . This field is related to the external applied field E0 by the equation E L = (3ϵ d /ϵ m + 2ϵ d )E0. The steady-state equation for the averaged external field is ∇2E0 + (ω2/c2)ϵ*E0 = 0, where ω is the frequency of the field, ϵ* is the dielectric function from the effective medium approximation, and it is obtained from the self-consistency relation4 〈ϵ(r) − ϵ*/ϵ(r) + 2ϵ*〉 = 0; the angular brackets denote an average taken over the ensemble of dielectric spheres distributed in a small volume. Using the slowly varying-envelope approximation we solve these equations for a distribution of grain radii and the affect this has on the effective optical nonlinearities. In particular, we show its effect on the optical bistability for these composite systems.